Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            ArrayList<String> list=new ArrayList<>();
            int n=input.nextInt();
            int m=input.nextInt();
            int a[][]=new int[n][m];
            for(int i=0;i<n;i++)
            {
                for(int j=0;j<m;j++)
                {
                    a[i][j]=input.nextInt();
                }
            }
            if(n<=m)
            {
                int arr[][]=new int[n][m];
                int minRow[]=new int[n];
                for(int i=0;i<n;i++)
                {
                    int min=Integer.MAX_VALUE;
                    for(int j=0;j<m;j++)
                    {
                        min=Math.min(min,a[i][j]);
                    }
                    for(int j=0;j<min;j++)
                    {
                        list.add("row "+(i+1));
                    }
                    minRow[i]=min;
                }
                int flag=0;
                for(int i=0;i<m;i++)
                {
                    HashSet<Integer> set=new HashSet<>();
                    for(int j=0;j<n;j++)
                    {
                        set.add(a[j][i]-minRow[j]);
                    }
                    if(set.size()>1)
                    {
                        flag=1;
                        break;
                    }
                    else
                    {
                        int v=set.iterator().next();
                        for(int j=0;j<v;j++)
                        {
                            list.add("col "+(i+1));
                        }
                    }
                }
                if(flag==1)
                {
                    out.println(-1);
                }
                else
                {
                    out.println(list.size());
                    for(int i=0;i<list.size();i++)
                    {
                        out.println(list.get(i));
                    }
                }
            }
            else
            {
                int arr[][]=new int[n][m];
                int minCol[]=new int[n];
                for(int i=0;i<m;i++)
                {
                    int min=Integer.MAX_VALUE;
                    for(int j=0;j<n;j++)
                    {
                        min=Math.min(min,a[j][i]);
                    }
                    for(int j=0;j<min;j++)
                    {
                        list.add("col "+(i+1));
                    }
                    minCol[i]=min;
                }
                int flag=0;
                for(int i=0;i<n;i++)
                {
                    HashSet<Integer> set=new HashSet<>();
                    for(int j=0;j<m;j++)
                    {
                        set.add(a[i][j]-minCol[j]);
                    }
                    if(set.size()>1)
                    {
                        flag=1;
                        break;
                    }
                    else
                    {
                        int v=set.iterator().next();
                        for(int j=0;j<v;j++)
                        {
                            list.add("row "+(i+1));
                        }
                    }
                }
                if(flag==1)
                {
                    out.println(-1);
                }
                else
                {
                    out.println(list.size());
                    for(int i=0;i<list.size();i++)
                    {
                        out.println(list.get(i));
                    }
                }
            }
        }
        out.close();
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }
        long nextLong()
        {
            return Long.parseLong(next());
        }
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
        String nextLine()
        {
            String str="";
            try
            {
                str=br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}